# What are the asymptote(s) and hole(s), if any, of #f(x)= (3e^(x))/(2-2e^(x))#?

##### 1 Answer

There is a horizontal asymptote at

#### Explanation:

To understand how to find asymptotes, you have to understand the definition of asymptotes.

The definition of a vertical asymptote is

There is a vertical asymptote at

The definition of a horizontal asymptote is

One way to do this is by calculus using the L'Hospital's rule, but that is a bit too long to explain. An easier way is to just use sketchy math- both will give you the same answer in most cases.

To solve using sketchy math:

One assumption we can make is that 2 is negligible because infinity is so large so we just ignore it or set it equal to zero. (I know, not the best way to do math)

As you can see, you can cancel out the

So as f(x) goes to infinity or negative infinity, the value of the function will go to

There is a horizontal asymptote at

There are no holes because you can't cancel anything out from the top and bottom.

Here is the solution for the horizontal asymptote using L'Hopitals rule if you are curious: